65909 ÷ 4 = 16477 R1
Alright, let's work through the division of 65909 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 2:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 25 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 4

Step 3:
4 goes into 19 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 164
Subtract 16 from 19 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 4

Step 4:
4 goes into 30 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 1647
Subtract 28 from 30 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 4

Step 5:
4 goes into 29 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 16477
Subtract 28 from 29 to get 1.

The final result is 16477 with a remainder of 1.